Place the chicken breasts in a shallow pan or deep skillet and cover by about one inch with cold water. Bring to a simmer over medium heat, maintain the heat at a simmer, and poach the breasts for 10 to 12 minutes, depending on their size. Remove the pan from the heat and allow the chicken to cool to room temperature. When the chicken is cool, remove it from the stock (which can be strained and used for another purpose), remove and discard the skin and bones, and chop the meat finely.
Meanwhile, cook the bacon until it is crisp. Drain the bacon well and chop in roughly, by hand or in a food processor. Place the chopped bacon on paper towels and dry further, in a conventional oven on a low heat or in a microwave oven, until it separates into bits. This process may need to be repeated 2 or 3 times, depending on the fat content of the bacon used.
Place the Roquefort cheese in the freezer for about 15 minutes; then remove the cheese from the freezer and grate it, using a cheese or vegetable grater. Cut the tomatoes into small dice and sprinkle with salt and pepper. Halve, peel, and dice the avocados; sprinkle with salt and fresh lemon juice. Using a food processor, chop the greens finely, into 3/16 inch bits, but do not reduce them to mush. Finely chop the hard boiled eggs.
To assemble the salad, place all the greens in a large bowl and toss them together; spread the greens evenly in the bottom of the bowl. Arrange the bacon, egg, chicken, tomato, and cheese in strips across the greens; arrange the chopped avocado around the edge of the salad. Bring the salad to the table with the dressing alongside and toss together just before serving.
Blend together all ingredients except the oils. Using a whisk or food processor, combine the oils and add them in a very fine stream, continuing to whisk until the mixture is well combined. Chill and shake thoroughly before serving.
The ingredients can be prepared several hours in advance, covered, and kept in the refrigerator; remove the ingredients about 15 minutes before assembling the salad.